4578985000Maths and Inference Assignment

4578985000Maths and Inference Assignment

1015SCG Quantitative Reasoning

Trimester 3 2023

Weight: 30%

Due date: By Friday 22nd December 2023 (End of week 7)

1119505195580Your name here

Your name here

1120140313690sxxxxxxxsxxxxxxxName: Student number:

2721991274955X

00X

Third-to-last digit of student number:

2726436589280X

00X

Use this to determine which data set to use for Question 1. eg digit is 3, use bac3.csv; digit is 0, use bac0.csv.Write this at the top of your answer to Question 1.

Second-to-last digit of student number:

2727071595630X

00X

Use this to determine which data set to use for Question 2. eg digit is 5, use life5.csv, digit is 0, use life0.csvWrite this at the top of your answer to Question 2.

Last digit of student number:

Use this to determine which data set to use for Question 3. eg digit is 7, use workshop7.csv, digit is 0, use workshop0.csv Write this at the top of your answer to Question 3.

Instructions:

Please fill out the above information and enter your answers in this Word document.

If your submission is not in the format provided in this Word document, it will not be graded.

Please upload your final assignment as PDF to the submission point on the course site.

Use the correct csv file, if you use a different file, there will be mark penalty.

For each of the questions show your working explain how the calculations are done, what software and functions are used, show appropriate screenshots from the software.

Make sure all the plots have titles or captions, axes labels with units and a legend if applicable. The scatter plots should be used for discrete data, lines should be used for fits.

Pay attention to significant figures, especially when quoting the values with errors.

The assignment is out of 100 marks. Marks for each question are given with the question in square braces [ ] .

If you have any questions, please ask your demonstrators during the workshops or post your questions (but not answers or solutions) in the course Teams channel.

Question 1 [40 marks]

A lab has 10 different bacterial samples, but they all got mislabelled.

The growth of the bacteria in specific conditions is given by an exponential function Nt=N0ekt, where N0 is the initial number of bacteria (for the time t=0), N(t) is the number of bacteria after time t (measured in days), and k is the growth constant.

Values of the growth factor k are different for each type of bacteria and are given in the table.

Bacteria type Growth factor k (1/days) Dangerous level C(number of bacteria/cm3)

A 0.11 200

B 0.12 310

C 0.13 500

D 0.14 720

E 0.15 550

F 0.16 1020

G 0.17 1300

H 0.18 1560

I 0.19 2000

J 0.20 2500

You are given a random sample in the Petri dish with initially 100 organisms living in a jelly, and you are asked to determine which type of the bacteria it is. You decide to grow the sample, measuring the number of bacteria in your sample every day. Use the file bacx.csv, where x is third-to-last digit of your student number.

0194310Enter your answer here, expand the text box as needed.

00Enter your answer here, expand the text box as needed.

Plot the number of bacteria as a function of time. [5 marks]

We want to use regression on this data to find the values characterising the sample growth, but to do it we need linear data. What can you plot on the y axis instead the number of the organisms, so the plot becomes linear? Explain and show appropriate equations. [5 marks]

0175260Enter your answer here, expand the text box as needed.

00Enter your answer here, expand the text box as needed.

Use regression to fit the linearised data and find the R2 value, gradient with an error, intercept with an error and the residual standard error. Explain what each of these quantities means in the context of your data. [10 marks]

0174625Enter your answer here, expand the text box as needed.

00Enter your answer here, expand the text box as needed.

Find the growth constant k (with error) from the regression data. [2 marks]

0174625Enter your answer here, expand the text box as needed.

00Enter your answer here, expand the text box as needed.

Plot the linearised graph of the data with the fit. Comment on the shape of the plot and the fit. [5 marks]

0174625Enter your answer here, expand the text box as needed.

00Enter your answer here, expand the text box as needed.

From the regression data, identify which sample you got. Explain how you arrived at your conclusion. [5 marks]

0174625Enter your answer here, expand the text box as needed.

00Enter your answer here, expand the text box as needed.

In the table, you can find the dangerous level C of each of the bacteria populations in units of the number of bacteria per volume. The volume refers to the volume of the jelly in which the bacteria are growing. The Petri dish has d=10 cm diameter, and the jelly is h=5mm thick. After how many days will the number of bacteria in your sample exceed the dangerous level? [8 marks]

0174625Enter your answer here, expand the text box as needed.

00Enter your answer here, expand the text box as needed.

Question 2 [30 marks]

A research study was conducted to examine the differences between older and younger adults on perceived life satisfaction. Several older adults and several younger adults were given a life satisfaction test. Scores on the test range from 0 to 60, with high scores indicative of high life satisfaction, low scores indicative of low life satisfaction. The data are in the lifex.csv file, where x is the second-to-last digit of your student number.

Find the best estimates and the standard errors for the life satisfaction score for the old and young adults. [8 marks]

0174625Enter your answer here, expand the text box as needed.

00Enter your answer here, expand the text box as needed.

Plot the data for the old and young adults, where on the y axis is the life satisfaction score and the x axis is a person number. Add a line showing the average to both plots. What can you say about the data in each plot? How do two plots compare? Refer to the values from the previous part. [6 marks]

0174625Enter your answer here, expand the text box as needed.

00Enter your answer here, expand the text box as needed.

Can you say with 95% confidence interval that the life satisfaction scores are the same between these two groups? Show the calculations; explain how you compared the two groups. [8 marks]

0174625Enter your answer here, expand the text box as needed.

00Enter your answer here, expand the text box as needed.

The same experiment was conducted 20 years ago. In the life_x.csv file you have the best estimates of the life satisfaction score from this experiment. Compare if the life satisfaction scores for both old and young adults changed since the previous experiment, to statistical significance of 0.02. Show the calculations; explain how you compared the new and old results. [8 marks]

0174625Enter your answer here, expand the text box as needed.

00Enter your answer here, expand the text box as needed.

Question 3 [30 marks]

The data in the workshopx.csv file, where x is the last digit of your student number, gives the workshop attendance, workshop mark, assignment 1 mark, final exam mark, and overall course mark (which includes a component from quizzes held in workshops) for some course. We want to establish if there is any relationship between students attendance in workshops, performance in given assessment tasks, and the overall marks they get in the course. The data in the table gives the number of workshops students attended (/12 workshops), their mark from workshop quizzes (/10 marks), their mark in their first assignment (/50 marks), their mark in their exam (/48 marks), and their overall course mark (/100%).

Using regression, establish a linear relation between attendance (x-axis) and each of the marks (y-axis) and fill the table below. Include a scatter plot of overall mark against attendance, including the regression line of best fit. [15 marks]

Data R2 Slope

i.e. m Error in slope y-intercept i.e. c Error in y-intercept Residual standard error

Workshop Assignment 1 Exam Overall 0154940Enter your answer here and fill the table above, expand the text box as needed.

00Enter your answer here and fill the table above, expand the text box as needed.

Is a student's mark in Assignment 1 a useful indicator of how well they are likely to perform in the exam? Include relevant plot and briefly (in one or two sentences), explain your reasoning [5 marks]

0174625Enter your answer here, expand the text box as needed.

00Enter your answer here, expand the text box as needed.

How many workshops does the student has to attend to pass the course (this means getting overall mark >=50%)? What is the error in the number of workshops? [7 marks]

0174625Enter your answer here, expand the text box as needed.

00Enter your answer here, expand the text box as needed.

Using the regression model, on average, what is the change in overall course mark for each additional workshop a student attended, with an error range? Explain. [3 marks]

0174625Enter your answer here, expand the text box as needed.

00Enter your answer here, expand the text box as needed.